a circular disc of mass m and radius R is set into motion on a horizontal floor with a linear speed v in the forward direction and an angular speed omega=v/3r in clockwise direction as shown in figure.find the magnitude of the total angular momentum of the disc about the axis perpendicular to the plane of disc and passing trough the bottom most pt.

Dear Pratima,

A wheel rolling over a surface has both a linear and a rotational velocity. Suppose the angular velocity of the wheel is [omega]. The corresponding linear velocity of any point on the rim of the wheel is given by

where R is the radius of the wheel (see Figure 12.1). When the wheel is in contact with the ground, its bottom part is at rest with respect to the ground. This implies that besides a rotational motion the wheel experiences a linear motion with a velocity equal to + v_cm (see Figure 12.2). We conclude that the top of the wheel moves twice as fast as the center and the bottom of the wheel does not move at all.

Figure 12.2. Motion of wheel is sum of rotational and translational motion.

An alternative way of looking at the motion of a wheel is by regarding it as a pure rotation (with the same angular velocity [omega]) about an instantaneous stationary axis through the bottom of the wheel (point P, Figure 12.3).

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